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Popular >

(x+1)(x+2)(x+3)(x+6)=-x^2

Solution

(x + 1) (x + 2) (x + 3) (x + 6) = - x^{2}

Solution

x \approx - 1.26794 \dots, x \approx - 1.26794 \dots, x \approx - 4.73205 \dots, x = - \frac{3691}{780}

+1

Decimal Notation

x = - 1.26794 \dots, x = - 1.26794 \dots, x = - 4.73205 \dots, x = - 4.73205 \dots

Solution steps

(x + 1) (x + 2) (x + 3) (x + 6) = - x^{2}

Expand

(x + 1) (x + 2) (x + 3) (x + 6) : x^{4} + 12 x^{3} + 47 x^{2} + 72 x + 36

x^{4} + 12 x^{3} + 47 x^{2} + 72 x + 36 = - x^{2}

Move

x^{2}

to the left side

x^{4} + 12 x^{3} + 48 x^{2} + 72 x + 36 = 0

Find one solution for

x^{4} + 12 x^{3} + 48 x^{2} + 72 x + 36 = 0

using Newton-Raphson:

x \approx - 1.26794 \dots

Apply long division:

\frac{x ^{4} + 12 x ^{3} + 48 x ^{2} + 72 x + 36}{x + 1.26794 \dots} = x^{3} + 10.73205 \dots x^{2} + 34.39230 \dots x + 28.39231 \dots

x^{3} + 10.73205 \dots x^{2} + 34.39230 \dots x + 28.39231 \dots \approx 0

Find one solution for

x^{3} + 10.73205 \dots x^{2} + 34.39230 \dots x + 28.39231 \dots = 0

using Newton-Raphson:

x \approx - 1.26794 \dots

Apply long division:

\frac{x ^{3} + 10.73205 \dots x ^{2} + 34.39230 \dots x + 28.39231 \dots}{x + 1.26794 \dots} = x^{2} + 9.46410 \dots x + 22.39230 \dots

x^{2} + 9.46410 \dots x + 22.39230 \dots \approx 0

Find one solution for

x^{2} + 9.46410 \dots x + 22.39230 \dots = 0

using Newton-Raphson:

x \approx - 4.73205 \dots

Apply long division:

\frac{x ^{2} + 9.46410 \dots x + 22.39230 \dots}{x + 4.73205 \dots} = x + 4.73205 \dots

x + 4.73205 \dots \approx 0

x \approx - 4.73205 \dots

Approximate to algebraic form

x = - \frac{3691}{780}

The solutions are

x \approx - 1.26794 \dots, x \approx - 1.26794 \dots, x \approx - 4.73205 \dots, x = - \frac{3691}{780}

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solvefor y,A=(ky^4)/S solve for

y, A = \frac{k y ^{4}}{S}

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(x^2+2x-4)(x^2-x-32)=0

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